I have implemented WooCommerce as the eCommerce solution for clients' WordPress (WP) based websites. It is a simple and easy to use solution for managing products, inventory, pricing, and easily integrates into WP's backend for managing the content of all of the above.
Payment methods - for a native experience you're basically restricted to using Stripe, Paypal, or Square to accept payments. This has been an issue for clients I've worked with that already have a preferred payment gateway vendor. There are integrations you can use, but this leads to either an iFrame checkout experience, or worse a completely separate site - not ideal.
This is not strictly about WooCommerce, but the ease of use of the product management backend is very dependent on the how well your WP theme integrates with it. I'd recommend using Themes specifically built to be a WooCommerce Shop. Trying to fit WooCommerce in after the fact to a theme not designed for it initially can be a little confusing.
I haven't used Shopify's WP integration, but I have built a Shopify site through their own platform. I found the CMS of WP to be more straight forward and intuitive, but it may be because I have a lot of WP experience. Shopify's CMS is certainly not a WP clone... In terms of the shop management, Shopify is certainly just as easy to use as WooCommerce, but WP's inherent flexibility makes creating and branding your shop much easier with the combo of Woo and WP than just using Shopify by itself.
For a WP site, WooCommerce is basically the industry standard for eCommerce. If you've got an existing site that you're adding a shop, I'd recommend doing a major redesign to make the site a WooCommerce theme site.
I know Shopify has WP integration to let you sell products from your WP site, but I don't personally have experience doing that. I know Shopify has more native payment gateways than WooCommerce does, so if using your preferred payment gateway is a hard requirement, you may be better off exploring Shopify.